On uniform opial condition and uniform Kadec-Klee property in Banach and metric spaces

Nonlinear Analysis, Theory, Methods and Applications

Volumn 26, Issue 10, 1996, Pages 1733-1748

  Khamsi, Mohamed Amine ^a  

^a UNIVERSITY OF TEXAS AT EL PASO   (United States)

Author keywords

Fixed point property; Hyperbolic metric spaces; Kadec Klee property; Normal structure property; Opial condition

Indexed keywords

EID: 0001763524     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/0362-546X(94)00216-5     Document Type: Article

References (42)

1. BESBES M., Points fixes et theoremes ergodiques dans les aspaces de Banach, These de Doctorat de L'Universite Paris 6 (1991).
2. BESBES M., DILWORTH S., DOWLING P. & LENNARD C., New convexity and fixed point properties in Hardy and Lebesgue-Bochner spaces (to appear).
3. KHAMSI M. A., Normal structure for Banach spaces with Schauder decomposition, Canad. Math. Bull. 32, 344-351 (1989).
4. KUCZUMOW T. & REICH S., Opial's property and James' quasi-reflexive spaces (to appear).
5. 1, Studio math. 100(2), 95-108 (1991).
6. BENAVIDES T. D., On an example of W. L. Bynum (to appear).
7. BROWDER F. E., Nonexpansive nonlinear operators in a Banach space. Proc. Natn. Acad. Sci. USA 54, 1041-1044 (1965).
8. GOHDE D., Zum Pinzip der kontraktiven abbildung, Math. Nachr. 30, 251-258 (1965).
9. KIRK W. A., Nonexpansive mappings in metric and Banach spaces. Rend. Sem. Fis. Milano 61, 133-144 (1981).
10. LIM T. C., Asymptotic centers and nonexpansive mappings in some conjugate spaces, Pac. J. Math. 90, 135-143 (1980).
11. DYE J., KHAMSI M. A. & REICH S., Random products of contractions in Banach spaces, Trans. Am. math. Soc. 325(1), 87-99 (1991).
12. BREZIS H. & LIEB E., A relation between pointwise convergence of functions and convergence of functionals, Proc. Am. math. Soc. 88, 486-490 (1983).
13. SIMON B., Convergence in trace ideals, Proc. Am. Math. Soc. 83, 39-43 (1981).
14. SIMS B., Fixed points of nonexpansive maps on weak and weak*-compact sets, Queen's University of Kingston, Lecture Notes (1982).
15. ARAZY A., More on convergence in unitary matrix spaces, Proc. Am. math. Soc. 83(1), 44-48 (1981).
16. 1, Pac. J. Math. 8, 467-485 (1958).
17. N. Springer, Berlin (1980).
18. 1-spaces, Canad. J. Math. 41, 882-900 (1989).
19. ANDREW A., James quasi-reflexive space is not ismorphic to any subspace of its dual, Israel J. Math. 38, 276-282 (1981).
20. JAMES R. C., Bases and reflexivity of Banach spaces, Ann. Math. 52, 518-527 (1950).
21. JAMES R. C., A nonreflexive Banach space isometric with its second cunjugate space, Proc. nat. Acad. Sci. USA 37, 134-137 (1951).
22. KARLOVITZ L., On nonexpansive mappings, Proc. Am. math. Soc. 55, 321-325 (1976).
23. KUCZUMOW T., Weak convergence theorems for nonexpansive mappings and semi-groups in Banach spaces with Opial's property, Proc. Am. math. Soc. 93, 430-432 (1985).
24. Opial Z., Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Am. math. Soc. 73, 591-597 (1967).
25. Opial Z., Nonexpansive and Monotone Mappings in Banach Spaces, Lecture Notes 67-1. Center for Dynamical Systems, Brown University, Providence, R. I. (1967).
26. PRUS S., Banach spaces with the uniform Opial property, Nonlinear Analysis 18, 697-704 (1992).
27. VAN DULST D. & SIMS B, Fixed points of nonexpansive mappings and Chebyshev centers in Banach spaces with norms of type (KK), Banach Space Theory and its applications, Proc. Bucharest 1981, Lecture Notes in Math. 991, pp. 35-43. Springer, Berlin (1983).
28. HUFF R., Banach spaces which are nearly uniformly convex, Rocky Mount. J. Math. 10, 743-749 (1980).
29. VAN DULST D. & VALK DE V., (KK)-properties normal structure and fixed points nonexpansive mappings in Orlicz spaces, Canad. J. Math. 38, 728-750 (1986).
30. ISTRATESCU V. I. & PARTINGTON J. R., On nearly uniformly convex and K-uniformly convex spaces, Math. Proc. Cambridge Philo. Soc. 95, 325-327 (1984).
31. 1, C. r. Acad. Sci. Paris 311(I). 243-246 (1990)
32. BUSEMANN H., Spaces with non-positive curvature, Acta. Math. 80, 259-310 (1948).
33. GOEBEL K. & REICH S., Uniform convexity, Hyperbolic geometry and Nonexpansive mappings. Marcel Dekker, New York (1984).
34. AKSOY A. G. & KHAMSI M. A., Nonstandard Methods in Fixed Point Theory. Springer, New York (1990).
35. GOEBEL K. & KIRK W. A., Topics in Metric Fixed Theory. Cambridge University Press, Cambridge (1990).
36. BRUCK R., Properties of fixed point sets of nonexpansive mappings in Banach spaces, Trans. Am. math. Soc. 179, 251-262 (1973).
37. BAILLON J. B., Comportement asymptotique des contractions et semi-groups de contractions-Equations de Schrodinger nonlineairs et divers, Theses de Doctorat d'Etat, Universite Paris 6 (1978).
38. BRUCK R., A simple proof of the mean ergodic theorem for Banach spaces, Israel J. Math. 32, 107-116 (1979).
39. BRODSKII M. S. & MILMAN D. P., On the center of convex set, Dokl. Akad. Nauk. USSR 59, 837-840 (1948).
40. KIRK W. A., A fixed point theorem for mappings which do not increase distances, Am. Math. Monthly 71, 1004-1006. (1965).
41. PENOT J. P., Fixed point theorems without convexity, Bull. Soc. France. Mem. 60, 129-152 (1979).
42. KIRK W. A., An abstract fixed point theorem for nonexpansive mappings, Proc. Am. math. Soc. 82, 640-642 (1981).